Ciphergoth made a nifty web toy based on his new trust metric. It's gotten so popular in just two days that it can't handle the load. From this and Friendster, it seems that it's extremely easy to get lots of users if you let them study their friends neigborhood, but it's hard to handle all the load.

Thinking about the first few people added to the metric, it's clear that ciphergoth's approach has some definite advantages over the one I gave in my last entry. Specifically, once you're done with the immediate friends list, the person who is a friend of a friend in the most ways should be selected next. My approach most definitely does not do that.

When selecting the first friend of a friend, what we have is essentially a voting problem. Ciphergoth's approach tries to find the best next person by assuming honesty, while my approach tries to reduce the amount of dishonesty by selecting the next person in as non-gameable a way as possible. Of these two tradeoffs, ciphergoth's seems to be the more appealing. This analysis indicates that maybe a condorcet style approach to picking the next person will achieve the best of both approachs. I'll have to think about that.

Minefield

Minefield is a game involving infinite numbers for two players.

Both players write down an infinite number (assuming the axiomatic basis ZF). They then both reveal what number they wrote down.

Both players now have a set amount of time to come up with a challenge to the other person's number. This can be done either by showing that the statement of the existence of the other person's infinite causes a contradiction, or by showing that your infinite is at least as large as the other person's.

If exactly one player shows that the other person's number causes an inconsistency, then that person wins. Otherwise, if exactly one person shows that their infinite is at least as big as the other person's, then that person wins. Otherwise the game is a do-over. In the case where someone should win by being larger, the opponent has an opportunity once they see the proof to challenge the consistency of the other player's number. This is to prevent the cheap trick of saying 'my number is inconsistent, therefore all statements are true, so it's at least as large as yours.

This game can be played, although it's a bit odd. Mostly I've thought of it as a way of getting a visceral sense of how very large infinites work.

Triumvirate

The 'degenerate' case of my game second best is actually the most interesting. Three players each write down either a 0 or 1, then all reveal what they wrote down. If they all wrote down the same number, then they all get one point. Otherwise, the player who wrote down the number which is in the minority gets three points. I'm calling this game triumvirate.

In triumvirate, two players can gang up on the third one by putting down different numbers, but then the third player can pick which one of them will win, and thus easily bully around either of them. I believe that triumvirate gets to the heart of what's difficult about multi-player, zero-sum games in much the same way that prisoner's dilemma gets to the heart of what's difficult about two-player, non-zero-sum games.